3 research outputs found
Topological edge state lasers based on photonic Su-Schrieffer-Heeger lattices
ํ์๋
ผ๋ฌธ (๋ฐ์ฌ) -- ์์ธ๋ํ๊ต ๋ํ์ : ์์ฐ๊ณผํ๋ํ ๋ฌผ๋ฆฌยท์ฒ๋ฌธํ๋ถ(๋ฌผ๋ฆฌํ์ ๊ณต), 2020. 8. ์ ํ์.Topological phases of matter opened the era of quantum materials by suggesting new states of matter. In particular, topological insulators are insulating in the bulk, but simultaneously the surface is conducting and the flow of surface electrons is topologically protected, so that scattering due to imperfections can be suppressed. These characteristics are expected to be useful for the development of spintronic devices or for stable information storage in quantum computers. On the other hand, the discovery in the fields of condensed matter has become another cornerstone for studying topological properties in other wave-particle systems such as light. In the case of the topological edge state of light, since it can be protected from backscattering due to imperfections as in the case of the electrons in the topological insulators, it is expected to be utilized in high-efficiency optical waveguides, couplers, and so on.
Many studies on topological photonics have been conducted to observe the propagation characteristics of light, such as time-reversal symmetry broken edge states using a magnetic field, and spin-protected edge states using dedicatedly designed pseudospin of light. Lasing action from topological edge states has not been studied as much as passive (transport) properties. In the case of previous studies on the topological lasers mainly utilizing the microring resonator, the sizes of the device and the mode are dozens of micrometers. However, by using a photonic crystal resonator, the mode can be reduced to a wavelength scale, and a single mode oscillation is feasible due to the small mode size. Therefore, if an edge state laser using a photonic crystal resonator is developed, it is expected to be a new turning point in the study of the topological edge state lasers. In addition, the photonic crystal resonators usually suffer from process imperfections due to its small feature size. The topological edge state is relatively less sensitive to the disorder caused by such process variations, and thus the yield improvement of the optical device can be expected.
In this thesis, for the first research topic, a robust topological edge state which is formed in a finite chain of photonic crystal (PhC) nanocavities combined with the Su-Schrieffer-Heeger (SSH) model is theoretically and experimentally demonstrated. We implement the model by arranging the same PhC nanocavities in an SSH dimer chain configuration composed of InAsP / InP multiple quantum well (MQW) epilayers, and demonstrate lasing behavior in relevant topological edge state and bulk state. In addition, the presence and robustness of TES is demonstrated by spectral analysis as well as direct visualization of the corresponding modal pattern using near-field optical microscopy techniques.
For the second research topic, inspired by novel higher-order topological insulator concept, we fabricate a 2D SSH-like topological photonic crystal structure using a InGaAsP MQW semiconductor optical gain material and confirm laser oscillations in multiple dimensional topological states existing in the structure. It is proved through spectral analysis and emission imaging that various lasers are selectively excited by varying the position of the pump light in a single photonic crystal device.
Finally, brief results of a valley edge mode laser are introduced. Valley edge modes which exist at the interface of two inversion symmetry-broken valley photonic crystals are utilized to form a ring cavity, which is enabled by topological protection of edge modes from sharp bends along the interface waveguide. Lasing action from the ring cavity is demonstrated and the fact that the formation of the ring cavity is truly a fruit of topological protection of the edge modes is confirmed by comparing with a trivial cavity laser.๋ฌผ์ง์ ์์์ ์ํ๋ ๊ธฐ์กด์ ์์๋ ์๋ก์ด ๋ฌผ์ง์ ์ํ๋ฅผ ์ ์ํจ์ผ๋ก์จ ์์ ๋ฌผ์ง์ ์๋๋ฅผ ์ด์๋ค. ํนํ, ์์๋ถ๋์ฒด๋ ๋ด๋ถ๊ฐ ๋ถ๋์ฒด์ธ ๋์์ ๋์ฒด์ธ ํ๋ฉด์ ๊ฐ์ง๊ณ ์์ผ๋ฉฐ ํ๋ฉด์์์ ์ ์์ ํ๋ฆ์ ์์์ ์ผ๋ก ๋ณดํธ๋๋ฏ๋ก ๋ถ์์ ์ฑ์ ์ํ ์ฐ๋์ด ํฌ๊ฒ ๊ฐ์๋๋ค. ์ด๋ฌํ ํน์ง์ ์คํํธ๋ก๋ ์์ ๋๋ ์์ ์ปดํจํฐ์์์ ์์ ์ ์ธ ์ ๋ณด ์ ์ฅ์ ํ์ฉ๋ ๊ฒ์ผ๋ก ๊ธฐ๋๋๋ค. ํํธ, ์ด๋ฌํ ์์ง๋ฌผ์ง๋ฌผ๋ฆฌํ์์์ ๋ฐ๊ฒฌ์ ๋น๊ณผ ๊ฐ์ ๋ค๋ฅธ ํ๋ ์์คํ
์์์ ์์์ ์ํ๋ฅผ ์ํ ์ฐ๊ตฌ์ ํฌ์์ด ๋์๋ค. ์์๋ถ๋์ฒด ํ๋ฉด์ ์ ์์ ๋ง์ฐฌ๊ฐ์ง๋ก, ๋น์ ์์์ ๊ฐ์ฅ์๋ฆฌ ์ํ๋ ์ฐ๋์ผ๋ก๋ถํฐ ๋ณดํธ๋๊ณ , ์ด๋ฌํ ํน์ฑ์ ๊ณ ํจ์จ์ ๊ด๋ํ๋ก, ๊ด๊ฒฐํฉ๊ธฐ ๋ฑ์ ์์ฉ์ ๊ธฐ์ฌํ ๊ฒ์ผ๋ก ๊ธฐ๋๋๋ค.
์ง๊ธ๊น์ง์ ๋ง์ ์์๊ด์ํ ์ฐ๊ตฌ๋ ๋น์ ์ ํํน์ฑ์ ์ง์ค๋์ด ์์๋ค. ์๋ฅผ ๋ค๋ฉด, ์๊ฐ ๋ฐ์ ๋์นญ์ฑ์ด ๊นจ์ง ์์-ํ ๊ฐ์ฅ์๋ฆฌ ์ํ ๋๋ ์คํ์ผ๋ก๋ถํฐ ๋ณดํธ๋ ๊ฐ์ฅ์๋ฆฌ ์ํ๋ฅผ ํตํ ๋น์ ์ ํ๊ฐ ์ฐ๊ตฌ๋์๋ค. ์ด๋ฌํ ์๋์ ์์คํ
์ ๋นํด ๋ ์ด์ ๋ฐ์ง์ ๋ง์ด ์ฐ๊ตฌ๋์ง ์์๋ค. ๊ธฐ์กด์ ๋ช๋ช ์์์ ๊ฐ์ฅ์๋ฆฌ ์ํ๋ฅผ ์ด์ฉํ ๋ ์ด์ ์ฐ๊ตฌ๋ ๋ง์ดํฌ๋ก๋ง ๊ณต์ง๊ธฐ๋ฅผ ์ด์ฉํ์ฌ์ ์์์ ํฌ๊ธฐ๊ฐ ๋งค์ฐ ํฌ๋ค๋ ๋จ์ ์ด ์์๋ค. ํ์ฅ-์ค์ผ์ผ์ ๊ด์๊ฒฐ์ ๊ตฌ์กฐ์์ ์์์ ๊ฐ์ฅ์๋ฆฌ ์ํ๋ฅผ ํ์ธํ๊ณ ์ด๋ฅผ ์ด์ฉํ ๋ ์ด์ ์์๋ฅผ ๊ฐ๋ฐํ๋ค๋ฉด ํฅ์๋ ๊ด ์ง์ ํ๋ก๋ ์์์ ๋น-๋ฌผ์ง ์ํธ์์ฉ์ ์ฐ๊ตฌํ ์ ์๋ ๊ธฐ๋ฐ์ด ๋ ๊ฒ์ผ๋ก ๊ธฐ๋ํ๋ค. ๋ฟ๋ง ์๋๋ผ, ๊ด์์์ ํฌ๊ธฐ๊ฐ ์์์ง์๋ก ๊ณต์ ์์ ์ค์ฐจ์ ์ํ ์ฑ๋ฅ ํธ์ฐจ๊ฐ ์ปค์ง๋๋ฐ, ์์์ ๊ฐ์ฅ์๋ฆฌ ์ํ๋ ์ด๋ฌํ ์ํฉ์์ ํด๊ฒฐ์ฑ
์ด ๋ ๊ฒ์ผ๋ก ๊ธฐ๋๋๋ค.
์ด ๋
ผ๋ฌธ์์๋, ์ฒซ ๋ฒ์งธ๋ก, ๊ด์๊ฒฐ์ ๊ณต์ง๊ธฐ ๋ฐฐ์ด์ ํตํ ์์์ ๊ฐ์ฅ์๋ฆฌ ์ํ์์์ ๋ ์ด์ ๋ฐ์ง์ ์์ฐํ์๋ค. Su-Schrieffer-Heeger ๋ชจ๋ธ์ ๊ธฐ๋ฐํ ๋ฐฐ์ด๊ณผ ๋ค์ค์์์ฐ๋ฌผ ๊ด์ด๋ ๋ฌผ์ง์ ์ด์ฉํ์ฌ ์์์ ์ผ๋ก ๋น์๋ช
ํ ๋ฐฐ์ด์์ ์์์ ๊ฐ์ฅ์๋ฆฌ ์ํ๊ฐ ๋ ์ด์ ๋ฐ์ง์ ํตํด์ ํ์ธ๋์๋ค. ๊ทผ์ ์ฅ ์ธก์ ์ ํตํด ๋ชจ๋ ๋ถํฌ๋ฅผ ์ง์ ์ ์ผ๋ก ๊ด์ฐฐํจ์ผ๋ก์จ ๊ด๋ชจ๋์ ๊ธฐ์์ ํ์ธํ ์ ์์๊ณ , ๊ณต์ ์ ๋ฌด์ง์๋ก๋ถํฐ ๊ฐ์ฅ์๋ฆฌ ์ํ๊ฐ ์๋์ ์ผ๋ก ๊ฒฌ๊ณ ํจ์ ํ์ธํ์๋ค.
๋ ๋ฒ์งธ๋ก, 2์ฐจ์ ๊ด์๊ฒฐ์ ์์์ ๊ณ ์ฐจ์ ์์์ ๋ถ๋์ฒด ์๋ฆฌ์ ์ํ ๊ณ์ธต์ ๊ฐ์ฅ์๋ฆฌ ์ํ์์์ ๋ ์ด์ ๋ฐ์ง์ ์์ฐํ์๋ค. 2์ฐจ์ SSH ๋ฐฐ์ด๊ณผ ์ ์ฌํ ํํ๋ก ๊ด์๊ฒฐ์ ์ ๋์์ธํ์๊ณ , ๊ด์ด๋ ๋ฌผ์ง์ ์ด์ฉํ์ฌ ์์น์ ๋ํด ์ ํ์ ์ธ ๊ดํํ์ ํตํด ๋ค์ํ ์ํ์์์ ๋ ์ด์ ๋ฐ์ง์ ํ์ธํ์๋ค. ๊ฐ ์ํ์์์ ๋ ์ด์ ํน์ฑ์ ์คํํธ๋ผ๊ณผ ์ด๋ฏธ์ง ๋ถ์์ ํตํด์ ์กฐ์ฌํ์๋ค.
๋ง์ง๋ง์ผ๋ก, valley ๊ฐ์ฅ์๋ฆฌ ์ํ๋ฅผ ์ด์ฉํ ๋ง ๊ณต์ง๊ธฐ์์์ ๋ ์ด์ ๋ฐ์ง์ ์์ฐํ์๋ค. ๊ณต๊ฐ ๋ฐ์ ๋์นญ์ฑ์ด ๊นจ์ด์ง ๊ตฌ์กฐ์์๋ valley๊ฐ ๋ณดํธ๋ ๊ฐ์ฅ์๋ฆฌ ์ํ๊ฐ ๋ํ๋ ์ ์๊ณ valley๊ฐ ์ฐ๋์ด ์ ์ ์ํฉ์์๋ ์ ํ ํน์ฑ์ด ๋ณดํธ๋์ด ๊ตฌ์กฐ์ ๋ณํ์ ์ํ ํ๋ฐฉ์ฐ๋์ด ๋งค์ฐ ๋ฎ์์ง๋ค. ์ด๋ฅผ ์ด์ฉํ์ฌ ๊ธ๊ฒฉํ ๊บพ์์ ๊ฐ์ง valley ๊ฐ์ฅ์๋ฆฌ ๋ชจ๋๋ฅผ ์ด์ด์ ๋ง ํํ๋ก ๊ณต์ง๊ธฐ๋ฅผ ์ ์ํ์๊ณ ์ค์ ๋ก ์์์ ์ผ๋ก ๋ณดํธ๋ ํน์ฑ์ ์ํด ๋ ์ด์ ๋ฐ์ง์ด ๊ฐ๋ฅํ ๊ฒ์ ์์์ ์ผ๋ก ๋ณดํธ๋์ง ์์ ์๋ช
ํ ๋ง ๊ณต์ง๊ธฐ์์ ๋น๊ต๋ฅผ ํตํด ํ์ธํ์๋ค.Chapter 1. Introduction ๏ผ
1.1. Photonic crystals and photonic crystal lasers ๏ผ
1.1.1. Introduction to the photonic crystal ๏ผ
1.1.2. Scaling property of electrodynamics ๏ผ
1.1.3. Photonic band structure ๏ผ
1.1.4. Photonic crystal band edge lasers ๏ผ
1.1.5. Photonic crystal cavity lasers ๏ผ๏ผ
1.2. Topological photonics ๏ผ๏ผ
1.2.1. Topological Insulator and topological band theory ๏ผ๏ผ
1.2.2. Topological edge states ๏ผ๏ผ
1.2.3. Topological photonics ๏ผ๏ผ
1.2.4. Topological photonic crystal lasers ๏ผ๏ผ
1.3. Outline of the Manuscript ๏ผ๏ผ
Chapter 2. Edge mode lasing in a photonic crystal cavity SSH array ๏ผ๏ผ
2.1. Introduction ๏ผ๏ผ
2.1.1. Photonic Su-Schrieffer-Heeger model ๏ผ๏ผ
2.1.2. Lasing in photonic SSH structures ๏ผ๏ผ
2.1.3. Performance fluctuation on a photonic crystal cavity ๏ผ๏ผ
2.2. Result ๏ผ๏ผ
2.2.1. Photonic crystal cavity SSH array ๏ผ๏ผ
2.2.2. Coupling strength control of coupled photonic crystal L3 cavities ๏ผ๏ผ
2.2.3. Band structure calculation ๏ผ๏ผ
2.2.4. Topological invariant calculation ๏ผ๏ผ
2.2.5. Finite lattice simulation ๏ผ๏ผ
2.2.6. Coupling-induced resonance shift ๏ผ๏ผ
2.2.7. Localization of the edge state ๏ผ๏ผ
2.2.8. Sample fabrication ๏ผ๏ผ
2.2.9 Micro-photoluminescence measurement ๏ผ๏ผ
2.2.10. Near-field scanning microscope measurement ๏ผ๏ผ
2.2.11. Lasing characteristics of the edge and bulk modes ๏ผ๏ผ
2.2.12. Spontaneous emission factor of the edge mode ๏ผ๏ผ
2.2.13. Chiral symmetry ๏ผ๏ผ
2.2.14. Robustness of the edge state ๏ผ๏ผ
2.2.15. Edge states in topological kink ๏ผ๏ผ
2.3. Conclusion ๏ผ๏ผ
Chapter 3. Higher-order topological edge states lasers ๏ผ๏ผ
3.1. Introduction ๏ผ๏ผ
3.1.1. 2D SSH lattices ๏ผ๏ผ
3.1.2. Higher order topological insulators ๏ผ๏ผ
3.1.3. Photonic crystal HOTIs ๏ผ๏ผ
3.2. Result and discussion ๏ผ๏ผ
3.2.1. Band structure calculation ๏ผ๏ผ
3.2.2. Hierarchical topology ๏ผ๏ผ
3.2.3. Edge state simulations ๏ผ๏ผ
3.2.4. Device fabrication ๏ผ๏ผ
3.2.5. Photoluminescence measurement ๏ผ๏ผ
3.2.6. Lasing characteristics ๏ผ๏ผ
3.2.7. Origin of in-gap corner states ๏ผ๏ผ
3.3. Conclusions ๏ผ๏ผ
Chapter 4. Preliminary results of a valley edge mode laser. ๏ผ๏ผ
4.1. Introduction to valley photonic crystals ๏ผ๏ผ
4.2. Result and discussion ๏ผ๏ผ
4.2.1. Band structure of valley photonic crystals ๏ผ๏ผ
4.2.2. VPC laser ๏ผ๏ผ
4.2.3. Comparison with a trivial cavity laser ๏ผ๏ผ
4.2.4. FSR analysis ๏ผ๏ผ
4.2.5. Structural disorder simulation ๏ผ๏ผ
4.3. Conclusions ๏ผ๏ผ๏ผ
Chapter 5. Conclusion and Perspective ๏ผ๏ผ๏ผ
References ๏ผ๏ผ๏ผ
Abstract in Korean ๏ผ๏ผ๏ผDocto